Powers of ten and measurement scale

Metric prefixes express powers of ten. Convert to a common unit before comparing measurements. Squared and cubed units require squared and cubed conversion factors.

Example

A length of \(35\,\mu\text{m}\) is \(35\times10^{-6}\text{ m}=3.5\times10^{-5}\text{ m}\).

Since \(1\text{ cm}=10^{-2}\text{ m}\), \(1\text{ cm}^2=10^{-4}\text{ m}^2\), so \(240\text{ cm}^2=2.4\times10^{-2}\text{ m}^2\).

An exponent must apply to the entire unit conversion: \(1\text{ cm}^3=(10^{-2}\text{ m})^3=10^{-6}\text{ m}^3\).